Square Root of 1849

The square root of 1849 is a number whose square is 1849. The square of 1849 in radical form is written as √1849 and in the exponential form it is written as (1849)^½. The square root of 1849 is the solution of the equation x² – 1849 = 0. In this article, we shall learn how to calculate the square root of 1849 using the prime factorisation and long division method.

Learn more about square and square roots.

What is Square Root of 1849?

The square root of 1849 is a number which is when multiplied twice by itself gives the answer 1849. The number 1849 is a perfect square as we can find integers 43 and –43 whose square is 1849.

Let us show how roots of the quadratic equation x² – 1849 = 0, is the square roots of 1849

x² – 1849 = 0

⇒ x² = 1849

Taking square roots on both sides, we get

⇒ x = √1849

⇒ x = ± 43

Also read: Properties of square numbers.

How to Find the Square Root of 1849?

Now, we shall find the square root of 1849 using the prime factorisation and long division method.

Prime Factorisation Method

To find the square root of 1849 by the prime factorisation method, we first prime factorise 1849 and then make pairs of two to get the square root.

Prime factorisation of 1849 = 43 × 43

Square root of 1849 = √[43 × 43] = 43.

Long Division Method

To find the square root of 1849 by the long division method, we shall write 1849 as the dividend and pair its digits from right to left. Now, we shall calculate the square root of 1849 as follows:

To learn how to find the square root of any number long division method, click here.

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Solved Examples on Square Root of 1849

Example 1:

Find the length and breadth of a rectangular plot whose area is 5547 m² and length is thrice its breadth.

Solution:

Let ‘b’ be the breadth of the rectangular plot

Length of the rectangular plot = 3b.

Area of the rectangular plot = length × breadth = 5547

⇒ 3b × b = 5547

⇒ b² = 5547/3 = 1849

⇒ b = √1849 = 43 m

∴ the length of the rectangular plot = 3 × 43 = 129 m

And the breadth of the rectangular plot= 43 m.

Example 2:

Find the roots of the equation (x² + 1)/5 = 370.

Solution:

We have, (x² + 1)/5 = 370

⇒ x² + 1 = 1850

⇒ x² = 1849

⇒ x = √1849

⇒ x = ±43

Example 3:

Find the radius of a circle whose area is 1849𝜋 cm².

Solution:

Let r be the radius of the circle.

Area of the circle = 𝜋r² = 1849𝜋 cm²

⇒ r² = 1849

⇒ r = √1849 = 43 (taking positive root as length cannot be negative).

∴ the radius of the circle is 43 cm.